PET reconstruction based on optimal linear stochastic filtering

It turns out that the iterative approach is very attractive for image reconstruction in positron emission tomography (PET). Its reconstruction quality heavily depends on the accuracy of the measurement model, which consists of the projection matrix and the statistics of noise. Almost all of iterative approaches require that the projection matrix is exactly known a prior, which conflicts with the fact that it is impossible to obtain the exact projection matrix subject to a number of complicated and physical effects. Hence, in the paper we establish a more general measurement model where the projection matrix is disturbed by a Gaussian noise and provide a different PET reconstruction approach. It is based on the linear optimal filtering for stochastic system with multiplicative noise. The approach reconstructs the PET image effectively, whose performance is evaluated with the computer-synthesized Zubal-thorax-phantom.